Question

Figure as shown a rod $PQ$ of length $20.0cm$ and mass $200g$ suspended through a fixed point $O$ by two threads of length $20.0cm$ each. A magnetic field of strength $0.500T$ exists in the vicinity of the wire $PQ$ as shown in the figure. The wires connecting with $PQ$ with the battery are loose and exert no force on $PQ$.

(a) Find the tension in the threads when the switch $S$ is open. (b) A current of $2.0A$ is established when the switch $S$ is closed. Find the tension in the thread.

Answer 1

It is given that

$l=20cm=0.2m$

$M=200g=0.2Kg$

$B=0.5T$

(a) The tension in the threads when the switch S is open

$2T\cos 30=mg$

$2T\frac{\sqrt{3}}{2}=0.2\times 10$

$T=\frac{2}{\sqrt{3}}=1.154N$

(b) when the switch S is closed a current of 2.0A is established then tension in thread will be

$2T\cos 30=mg+ilB$

$2T\frac{\sqrt{3}}{2}=0.2\times 10+2\times 0.2\times 0.5$

$2T\frac{\sqrt{3}}{2}=2.2$

$T=1.27N$